# Maximum normal stress and shear stress

• Engineering
• Moara
In summary, the conversation discusses finding external reactions in A and B using only one equation. Once the reactions are found, the external moment can also be determined. The speakers suggest drawing diagrams of moments in each cross section to find the maximum moment, which can then be used to find the maximum normal stress. They also consider finding a general formula for the beam's displacement and using the given value to determine the reactions and maximum moment. Finally, they contemplate the end deflection if B was not present.
Moara
Homework Statement
A cantilever with elasticy modulus (##E = 13 \ GPa##) is subjected to the distribution of forces as in figure. The cross section T shaped is indicated in the figure. The moment of inertia with respect to the centroidal axis ##z## is ##1496.45 \cdot 10^6 \cdot mm^4##. In the absence of the distribution of forces, there is a lack of ##0.5 mm## between the bean and the mobile support. Knowing that the bean touches the support with the load distribution, find:
1) The maximum normal stress
2) The value of the maximum shear stress in the body
3) The deflection in the middle of the bean
Relevant Equations
##\sum{F_y} = 0##, ##\sum{M} = 0##
First, I am trying to find the external reactions in A and B, but I have only one equation relating ##V_A## and ##V_B##, what other relation could I use ?
Once I find the reactions, I can find the external moment as well. Then, I may draw the diagram of moments in each cross section and then find the maximum Moment. Using that ##\sigma = -My/I## I can find the maximum normal stress.

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Indeed, maybe we can try to find the general formula for the displacement of the beam and then impose that ##v(4) = -0.5 mm##. With that, I think we may find ##V_A, V_B, M_A## and find the diagram of moments, to find its maximum value

What would the end deflection be if B was not there?

Moara

## 1. What is maximum normal stress?

Maximum normal stress is the maximum amount of stress that a material can withstand before it reaches its breaking point. It is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (Pa).

## 2. How is maximum normal stress calculated?

Maximum normal stress is calculated by dividing the maximum force or load applied to a material by its cross-sectional area. This results in a stress value, which can then be compared to the material's ultimate tensile strength to determine if it will fail.

## 3. What factors can affect maximum normal stress?

There are several factors that can affect maximum normal stress, including the type and composition of the material, its temperature, and the presence of any defects or imperfections. Additionally, the method of applying the force or load can also impact the maximum normal stress.

## 4. What is shear stress?

Shear stress is a type of stress that occurs when two forces are applied parallel to each other in opposite directions, causing one part of a material to slide or shift relative to another part. It is typically measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (Pa).

## 5. How does shear stress differ from normal stress?

Normal stress is a type of stress that occurs when a force is applied perpendicular to the surface of a material, while shear stress occurs when forces are applied parallel to the surface. Normal stress results in a change in the length or volume of a material, while shear stress results in a change in its shape or orientation.

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